Where to apply if I am interested in Analysis and PDEs

[yaskhn3]

I am having some difficulty choosing where to apply for a Ph.D. I am mostly interested in Analysis and PDEs. I have to choose 10-12 schools from the following list:

Ambitious: Harvard, UCLA. UCB, MIT, Princeton, Columbia, Yale, Chicago, Cornell, NYU, Brown, Pennsylvania

Within reach: Michigan, Wisconsin-Madison, Gatech, UIUC, Purdue, Notre Dame, Rutgers, UCSD, Maryland

Could someone please suggest me about this? If you have any other recommendations, please let me know.

Thanks!

[Integreat]

I am having some difficulty choosing where to apply for a Ph.D. I am mostly interested in Analysis and PDEs. I have to choose 10-12 schools from the following list:

Ambitious: Harvard, UCLA. UCB, MIT, Princeton, Columbia, Yale, Chicago, Cornell, NYU, Brown, Pennsylvania

Within reach: Michigan, Wisconsin-Madison, Gatech, UIUC, Purdue, Notre Dame, Rutgers, UCSD, Maryland

Could someone please suggest me about this? If you have any other recommendations, please let me know.

Thanks!

Consider UT Austin and Stanford! Idk about Brown, Penn, ND, Yale, and Princeton. In my mind, Brown is geared more towards applied math. I'm not sure if Penn, ND, and Yale have many analysts. Princeton has analysts, but they're mostly geometric analysts from what I know. So if that's what you like then go for it.

[Sampaoli]

I would also consider Northwestern. They have one of the top programs in Analysis (Geometric Analysis and Probability) in the US. They do not require Math GRE according to their website.

[ponchan]

Absolutely include Minnesota